Matrix acidizing is a process used to increase the production rate of wells in hydrocarbon reservoirs. It includes the step of pumping an acid into an oil- or gas-producing well to increase the permeability of the formation through which hydrocarbon is produced and to remove some of the formation damage caused by the drilling and completion fluids and drill bits during the drilling and completion process.
The procedural techniques for pumping stimulation fluids down a wellbore to acidize a subterranean formation are well known. The person who designs such matrix acidizing treatments has available many useful tools to help design and implement the treatments, one of which is a computer program commonly referred to as an acid placement simulation model (a.k.a., matrix acidizing simulator, wormhole model). Most if not all commercial service companies that provide matrix acidizing services to the oilfield have one or more simulation models that their treatment designers use. One commercial matrix acidizing simulation model that is widely used by several service companies is known as StimCADE™. This commercial computer program is a matrix acidizing design, prediction, and treatment-monitoring program that was designed by Schlumberger Technology Corporation. All of the various simulation models use information available to the treatment designer concerning the formation to be treated and the various treatment fluids (and additives) in the calculations, and the program output is a pumping schedule that is used to pump the stimulation fluids into the wellbore. The text “Reservoir Stimulation,” Third Edition, Edited by Michael J. Economides and Kenneth G. Nolte, Published by John Wiley & Sons, (2000), is an excellent reference book for matrix acidizing and other well treatments.
Various mathematical models have been proposed in order to represent the flow of acid within the carbonate formations around the wellbore and the subsequent dissolution of the rock matrix where acid has invaded. Then, according to the prediction of these models, engineers can estimate how much the well will produce after treatment and, therefore, estimate whether a given treatment design will lead to the targeted production increase and optimize the design accordingly. The models proposed in the literature are developed to represent acid flow in radial flow, i.e. axisymmetric, conditions as could be observed in some particular conditions. But axisymmetric flow conditions are not always present. It would be a major advance to provide                a criterion to determine under which radial flow, i.e. axisymmetric flow, is relevant,        a method to solve acid flow when acid flow around the wellbore is not axisymmetric.        